Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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ram ex cylindris vel cylindri portionibus, vel
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mis</
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æqualium
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circumſcribi poſſe, cuius centrum
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grauitatis ſit propinquius puncto F, quàm punctum G: figu
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ræ enim ABC figura, qualem diximus circumſcribatur, cu
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ius reſiduum dempta figura ABC, ad figuram ABC mi
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norem habeat proportionem, quàm FG, ad GB, ſit autem
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figuræ circumſcriptæ centrum grauitatis K, nempe in axe,
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vel diametro BD. </
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>Dico
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lineam FK minorem eſſe
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quàm FG, atque adeo lon
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gitudine propoſita. </
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<
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>Quo
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niam enim F eſt centrum
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grauitatis figuræ ABC,
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erit centrum grauitatis
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K
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,
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figuræ circumſcriptæ ipſi
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ABC propinquius termi
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no B, quàm punctum F,
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ſed centrum grauitatis fi
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guræ ABC quòd eſt F, &
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figuræ circumſcriptæ, quod
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eſt K & eius reſidui dem
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pta figura ABC ſunt in communi axe, vel diametro BD;
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erit igitur dicti reſidui in linea BK, centrum grauitatis,
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quod ſit H. </
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<
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>Minor autem proportio eſt prædicti reſidui
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ad figuram ABC, hoc eſt ipſius FK ad KH, quàm FG
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ad GB, & multo minor, quàm FG ad GH; & compo
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nendo minor proportio FH ad HK, quàm FH ad HG;
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ergo KH maior erit, quàm GH; reliqua igitur F
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K
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mi
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nor, quàm FG atque adeo longitudine propoſita. </
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<
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ergo poteſt, quod proponebatur. </
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